Such a booster can be used particularly for boosting the braking of motor vehicles. In this application, the operation of such a booster is well known and can therefore be explained briefly as follows: in the rest phase, the two chambers are connected to a vacuum source; in the braking phase, air at atmospheric pressure is admitted into one of the chambers; the difference in pressure between the two chambers then gives rise to the displacement of the moving wall and consequently boosts the braking.
Document FR-B-2,334,862 describes a pneumatic booster in which a membrane is supported by a rigid plate comprising a cylindrical forwards extension at its outer edge for preventing the membrane, under the effect of the difference in pressure, from deforming towards the center of the booster and from hindering the movement of the plate. With such a design, the diameter of the plate remains limited by the diameter of the rear part of the casing. It follows that the active surface of the moving wall, that is to say the one on which the difference in pressure is exerted, is itself also limited by the rear part of the casing.